{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Community 1: Physics-informed KAN"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Disclaimer: This is uploaded from a github user, not the KAN authors. KAN authors did not writer this or proofread this carefully, hence are not responsible for mistakes in this notebook. If you have questions, please consult the github user who uploaded it. Thank you!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using device: cpu\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Step: 195 | Loss: 0.011: 100%|██████████| 200/200 [2:52:51<00:00, 51.86s/it]  \n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "from torch import autograd\n",
    "from torch.utils.tensorboard import SummaryWriter\n",
    "from tqdm import tqdm\n",
    "import matplotlib.pyplot as plt\n",
    "from kan import KAN, LBFGS\n",
    "\n",
    "device = torch.device(\"cpu\")\n",
    "print(\"Using device:\", device)\n",
    "\n",
    "rho = torch.tensor(1.0, device=device, requires_grad=False)\n",
    "nu = torch.tensor(0.01, device=device, requires_grad=False)\n",
    "eps = torch.tensor(1e-8, device=device, requires_grad=False)\n",
    "\n",
    "width, height = 10.0, 2.0\n",
    "num_points_x, num_points_y = 100, 20\n",
    "\n",
    "x = torch.linspace(0, width, num_points_x, device=device, requires_grad=False)\n",
    "y = torch.linspace(0, height, num_points_y, device=device, requires_grad=False)\n",
    "X, Y = torch.meshgrid(x, y, indexing='ij')\n",
    "coordinates = torch.stack([X.flatten(), Y.flatten()], dim=1).to(device)\n",
    "coordinates.requires_grad = True  # Ensure coordinates require grad\n",
    "\n",
    "model = KAN(width=[2,3,3, 3], grid=5, k=10, grid_eps=1.0,\n",
    "            noise_scale_base=0.25).to(device)\n",
    "\n",
    "def batch_jacobian(func, x, create_graph=False):\n",
    "    def _func_sum(x):\n",
    "        return func(x).sum(dim=0)\n",
    "    return autograd.functional.jacobian(_func_sum, x, create_graph=create_graph).permute(1, 0, 2)\n",
    "\n",
    "def batch_hessian(func, x):\n",
    "    jacobian = batch_jacobian(func, x, create_graph=True)\n",
    "    hessians = []\n",
    "    for i in range(jacobian.size(1)):\n",
    "        grad = autograd.grad(jacobian[:, i].sum(), x, create_graph=True, retain_graph=True)[0]\n",
    "        hessians.append(grad.unsqueeze(1))\n",
    "    return torch.cat(hessians, dim=1)\n",
    "\n",
    "def navier_stokes_residuals(coords):\n",
    "    coords = coords.clone().detach().requires_grad_(True)  # Ensure coords require grad\n",
    "    y_pred = model(coords)\n",
    "    grads = batch_jacobian(model, coords, create_graph=True)\n",
    "    hessians = batch_hessian(model, coords)\n",
    "\n",
    "    u, v, p = y_pred[:, 0], y_pred[:, 1], y_pred[:, 2]\n",
    "    u_x, u_y = grads[:, 0, 0], grads[:, 0, 1]\n",
    "    v_x, v_y = grads[:, 1, 0], grads[:, 1, 1]\n",
    "    p_x, p_y = grads[:, 2, 0], grads[:, 2, 1]\n",
    "\n",
    "    u_xx, u_yy = hessians[:, 0, 0], hessians[:, 0, 1]\n",
    "    v_xx, v_yy = hessians[:, 1, 0], hessians[:, 1, 1]\n",
    "\n",
    "    continuity = u_x + v_y + eps * p\n",
    "    x_momentum = u * u_x + v * u_y + (1 / rho) * p_x - nu * (u_xx + u_yy)\n",
    "    y_momentum = u * v_x + v * v_y + (1 / rho) * p_y - nu * (v_xx + v_yy)\n",
    "\n",
    "    no_slip_mask = (coords[:, 1] == 0) | (coords[:, 1] == height)\n",
    "    inlet_mask = (coords[:, 0] == 0)\n",
    "    outlet_mask = (coords[:, 0] == width)\n",
    "\n",
    "    no_slip_loss = torch.mean(u[no_slip_mask] ** 2 + v[no_slip_mask] ** 2)\n",
    "    inlet_loss = torch.mean((u[inlet_mask] - 1) ** 2)\n",
    "    outlet_pressure_loss = torch.mean(p[outlet_mask] ** 2)\n",
    "\n",
    "    bc_loss = no_slip_loss + inlet_loss + outlet_pressure_loss\n",
    "    total_loss = torch.mean(continuity ** 2 + x_momentum ** 2 + y_momentum ** 2) + bc_loss\n",
    "    return total_loss\n",
    "\n",
    "writer = SummaryWriter()\n",
    "\n",
    "def train():\n",
    "    optimizer = LBFGS(model.parameters(), lr=1,\n",
    "                      history_size=10, line_search_fn=\"strong_wolfe\", tolerance_grad=1e-32, tolerance_change=1e-32, tolerance_ys=1e-32)\n",
    "    \n",
    "    steps = 200 # 20 steps are enough\n",
    "    pbar = tqdm(range(steps), desc='Training Progress')\n",
    "\n",
    "    for step in pbar:\n",
    "        def closure():\n",
    "            optimizer.zero_grad()\n",
    "            loss = navier_stokes_residuals(coordinates)\n",
    "            loss.backward()\n",
    "            return loss\n",
    "\n",
    "        optimizer.step(closure)\n",
    "        if step % 5 == 0:\n",
    "            current_loss = closure().item()\n",
    "            pbar.set_description(\"Step: %d | Loss: %.3f\" %\n",
    "                                 (step, current_loss))\n",
    "            writer.add_scalar('Loss/train', current_loss, step)\n",
    "\n",
    "train()\n",
    "\n",
    "writer.close()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "u_pred = model(coordinates)[:, 0].detach().reshape(\n",
    "    num_points_x, num_points_y).T\n",
    "\n",
    "v_pred = model(coordinates)[:, 1].detach().reshape(\n",
    "    num_points_x, num_points_y).T\n",
    "\n",
    "\n",
    "magnitude = torch.sqrt(u_pred ** 2 + v_pred ** 2)\n",
    "\n",
    "plt.figure(figsize=(10, 5))  # Set the figure size as needed\n",
    "plt.imshow(magnitude, extent=(0, width, 0, height), origin='lower', cmap='viridis')\n",
    "plt.colorbar()  # Add a colorbar to show the magnitude scale\n",
    "plt.title('Velocity Magnitude Contour')\n",
    "plt.xlabel('Width')\n",
    "plt.ylabel('Height')\n",
    "plt.axis('equal')  # Ensure the plot has equal scaling\n",
    "plt.tight_layout()  # Adjust layout to prevent overlap\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x1000 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Extracting predictions\n",
    "u_pred = model(coordinates)[:, 0].detach().reshape(num_points_x, num_points_y).T\n",
    "v_pred = model(coordinates)[:, 1].detach().reshape(num_points_x, num_points_y).T\n",
    "p_pred = model(coordinates)[:, 2].detach().reshape(num_points_x, num_points_y).T\n",
    "\n",
    "# Velocity Magnitude\n",
    "magnitude = torch.sqrt(u_pred ** 2 + v_pred ** 2)\n",
    "\n",
    "# Plotting all subplots\n",
    "fig, axs = plt.subplots(2, 2, figsize=(15, 10))\n",
    "\n",
    "# Velocity Magnitude\n",
    "im0 = axs[0, 0].imshow(magnitude, extent=(0, width, 0, height), origin='lower', cmap='viridis')\n",
    "fig.colorbar(im0, ax=axs[0, 0])\n",
    "axs[0, 0].set_title('Velocity Magnitude Contour')\n",
    "axs[0, 0].set_xlabel('Width')\n",
    "axs[0, 0].set_ylabel('Height')\n",
    "axs[0, 0].axis('equal')\n",
    "\n",
    "# u Component\n",
    "im1 = axs[0, 1].imshow(u_pred, extent=(0, width, 0, height), origin='lower', cmap='coolwarm')\n",
    "fig.colorbar(im1, ax=axs[0, 1])\n",
    "axs[0, 1].set_title('u Component')\n",
    "axs[0, 1].set_xlabel('Width')\n",
    "axs[0, 1].set_ylabel('Height')\n",
    "axs[0, 1].axis('equal')\n",
    "\n",
    "# v Component\n",
    "im2 = axs[1, 0].imshow(v_pred, extent=(0, width, 0, height), origin='lower', cmap='coolwarm')\n",
    "fig.colorbar(im2, ax=axs[1, 0])\n",
    "axs[1, 0].set_title('v Component')\n",
    "axs[1, 0].set_xlabel('Width')\n",
    "axs[1, 0].set_ylabel('Height')\n",
    "axs[1, 0].axis('equal')\n",
    "\n",
    "# Pressure\n",
    "im3 = axs[1, 1].imshow(p_pred, extent=(0, width, 0, height), origin='lower', cmap='coolwarm')\n",
    "fig.colorbar(im3, ax=axs[1, 1])\n",
    "axs[1, 1].set_title('Pressure')\n",
    "axs[1, 1].set_xlabel('Width')\n",
    "axs[1, 1].set_ylabel('Height')\n",
    "axs[1, 1].axis('equal')\n",
    "\n",
    "plt.tight_layout()  # Adjust layout to prevent overlap\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x600 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
